$s$-wave scattering lengths for the ${}^7$Be+p system from an $\text{R}$-matrix analysis

Abstract

The astrophysical $S$-factor for the radiative proton capture reaction on ${}^7$Be ($S_{17}$) at low energies is affected by the $s$-wave scattering lengths. We report the measurement of elastic and inelastic scattering cross sections for the ${}^7$Be+p system in the center-of-mass energy range 0.474 - 2.740 MeV and center-of-mass angular range of 70${}^{\circ }$- 150${}^{\circ }$. A radioactive ${}^7$Be beam produced at Oak Ridge National Laboratory's (ORNL) Holifield Radioactive Ion Beam Facility was accelerated and bombarded a thin polypropylene (CH${}_2$)${}_{\text{n}}$ target. Scattered ions were detected in the segmented Silicon Detector Array. Using an $\text{R}$-matrix analysis of ORNL and Louvain-la-Neuve cross section data, the $s$-wave scattering lengths for channel spins 1 and 2 were determined to be 17.34${}_{-1.33}^{+1.11}$ and -3.18${}_{-0.50}^{+0.55}$ fm, respectively. The uncertainty in the $s$-wave scattering lengths reported in this work is smaller by a factor of 5-8 compared to the previous measurement, which may reduce the overall uncertainty in $S_{17}$ at zero energy. The level structure of ${}^8$B is discussed based upon the results from this work. Evidence for the existence of 0${}^{+}$ and 2${}^{+}$ levels in ${}^8$B at 1.9 and 2.21 MeV, respectively, is observed.